And Leads Me to Chaos
Theory
A major breakthrough in my journey was reading the book, Chaos,
The Making of a New Science, by Gleick. As it turned out, the
behavior of chaotic systems was familiar to me from work I did many
years ago with analog computers simulating nonlinear systems. But
at that time, no one had put the phenomenon on a solid theoretical
basics.
When I studied nonlinear systems at Wisconsin, everything was a
special case approach. If you could identify that this system was
a certain type for which the solution was known, fine. If not, you
were left to your own devices. There was no general theory for
nonlinear systems. Chaos theory changed all of that.
As Gleick explained how chaos theory was discovered by use of the
analog computer, I understood exactly what was being said. I felt
like I was a part of the discovery.
I immediately began digging into the application of chaos theory to
the market. To make a long story short, chaos theory does describe
the solar system, the stirring on the sun, our weather, and chaos
theory describes markets. It provided me with the keys that brought
all my other research together.
If I were to explain chaos theory to you, I'd tell you to think about
a bowl. If I take a ball and drop it into the bowl, it will roll
around and settle in the bottom. That is a linear system. It is a
very predictable system. Now if I take another bowl and slide it up
to the first one so that the very thin rims touch, I have a chaotic
system. If I take the ball and manage to balance it on the intersection
of the rims, the slightest motion will send that ball into one bowl
or the other. Whichever bowl the ball goes into, it will settle down
to a point of rest at the bottom of that bowl. The point where the
two rims touch is a boundary point between two regions. That
boundary point is called a "strange repellor". It is an unstable point
of balance between opposing forces. There are also stable points
of balance, called "strange attractors". All markets have such
points. We call them turning points.
A good example of a turning point- a strange attractor- in a social
system was the Tieneman Square event in China in May and June of 1989. Here
we had an incredible balance between the very powerful forces of freedom
and the forces of total control For almost a month, the forces balanced,
and then something tipped the balance. At just the right moment,
the Communists sent in a relatively small force, tipping the balance, and
the massacre of the protesting students ensued. The freedom movement
has been silent since.
That same chaotic behavior does happen in the market. I've
been able to find the lips of those bowls - the strange attractors. I
had to do some very deep theoretical work into how various cycles
combined. But the mental and computer work was well worth it.
Chaos Theory Pays Off
As evidence of the power of using chaos theory, look at Figure 1.
It shows two nonlinear boundaries on the S&P 500. At the point where
they converge in late December and early January is a strange attractor.
Knowing where this was made it easy to tell my clients to be looking
for a significant top between January 4th and 10th.
An even more exciting example in applying chaos theory is shown in
Figures 2 and 3.
In November 1989, I was advising clients that
"...the top is very near in the Nikkei." This was based on my
computation of the natural growth boundary curve for the Nikkei, which
originates on the day the index was started, and traces the upper
limit of its stable growth region. This curve is governed by an equation
that simply ceased to exist on December 27th, 1989. The endpoint
of this growth curve is a strange attractor.
Figure 3 shows a closeup of the Nikkei behavior just prior to and
after the strange attractor. The actual top of the Nikkei was December
29th, and was about 2000 points higher than computed. But the entry
into the new region of behavior, which occurs at strange attractors,
is very evident. It wasn't the Japanese election or interest
rate fears that topped the Nikkei. It was just the way the system
is built.
The Nikkei put warrants I recommended (and traded myself) tripled,
then doubled, for a 700 percent gain.
Is this incredible? Yes, it is. But I can assure you, every
step of the cause and effect relationship from planetary motion, to
solar radiation, to earth's magnetic field changes, to changes in
human physiology, to market motion can be scientifically verified. The
studies, the statistics, and the mathematics are all there. With the
addition of Chaos Theory, the behavior of it all is absolutely explainable.
Best of all, you can trade with it.